Improved amplitude preservation for prestack depth migration by inverse scattering theory

A prestack reverse time-migration image is not properly scaled with increasing depth. The main reason for the image being unscaled is the geometric spreading of the wavefield arising during the back-propagation of the measured data and the generation of the forward-modelled wavefields. This unscaled image can be enhanced by multiplying the inverse of the approximate Hessian appearing in the Gauss–Newton optimization technique. However, since the approximate Hessian is usually too expensive to compute for the general geological model, it can be used only for the simple background velocity model.We show that the pseudo-Hessian matrix can be used as a substitute for the approximate Hessian to enhance the faint images appearing at a later time in the 2D prestack reverse time-migration sections. We can construct the pseudo-Hessian matrix using the forward-modelled wavefields (which are used as virtual sources in the reverse time migration), by exploiting the uncorrelated structure of the forward-modelled wavefields and the impulse response function for the estimated diagonal of the approximate Hessian. Although it is also impossible to calculate directly the inverse of the pseudo-Hessian, when using the reciprocal of the pseudo-Hessian we can easily obtain the inverse of the pseudo-Hessian. As examples supporting our assertion, we present the results obtained by applying our method to 2D synthetic and real data collected on the Korean continental shelf.